What does the equation \(x^2 + y^2 + 2x + 1 = 0\) represent? Please explain.

A. a parabola
B. an ellipse
C. a point
D. a circle

The equation represents a circle.
If you factorise the equation, you get:
x 2 + y 2 + 2 x + 1 = 0 ( x + 1 ) 2 − 1 + ( y ) 2 = 0 ( x + 1 ) 2 + y 2 = 1
This final equation shows the equation of a circle, as a circle's equation is given as:
( x + a ) 2 + ( y + b ) 2 = r 2

Answered by ollieboyne | 2024-06-10

It a circle because, the equation is a degree 2 equation. That is squared.
The coefficient of x^2 and y^2 are the same.
There is no term term xy.
And a parabola is of the form y^2 = 4ax or x^2 = 4ay.
And an ellipse is of the form: (x^2)/(a^2) + (y^2)/(b^2) = 1.

Answered by olemakpadu | 2024-06-10

The equation x 2 + y 2 + 2 x + 1 = 0 represents a single point in the coordinate plane, specifically at ( − 1 , 0 ) . Therefore, the correct answer is option C. a point.
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Answered by ollieboyne | 2024-12-26